Microscopic and strongly microscopic sets on the plane. Fubini theorem and Fubini property

• Autorzy: Karasińska A. , Wagner-Bojakowska E.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce the notions of microscopic and strongly microscopic sets on the plane and obtain a result analogous to Fubini Theorem.

Słowa kluczowe

EN

microscopic set; strongly microscopic set on the plane; Fubini theorem; Fubini property

PL

twierdzenie Fubiniego; własność Fubiniego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 581--594
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Karasińska A.

• Faculty of Mathematics and Computer Science, University of Łódz, ul. Banacha 22, 90-238 Łódz, Poland

autor

Wagner-Bojakowska E.

• Faculty of Mathematics and Computer Science, University of Łódz, ul. Banacha 22, 90-238 Łódz, Poland

Bibliografia

• [1] J. Appell, E. D’Aniello, M. Väth, Some remarks on small sets, Ricerche Mat. 50 (2001), 255–274.
• [2] A. M. Bruckner, J. B. Bruckner, B. S. Thomson, Real Analysis, Prentice-Hall, New Jersey, 1997.
• [3] M. Filipczak, E. Wagner-Bojakowska, Remarks on small sets on the real line, Tatra Mt. Math. Publ. 42 (2009), 73–80.
• [4] R. Ger, On some functional equations with a restricted domain, Fund. Math. 89 (1975), 131–149.
• [5] A. Karasińska, E. Wagner-Bojakowska, Nowhere monotone functions and microscopic sets, Acta Math. Hungar. 120(3) (2008), 235–248.
• [6] A. Karasińska, E. Wagner-Bojakowska, Homeomorphisms of linear and planar sets of the first category into microscopic sets, Topology Appl. 159(7) (2012), 1894–1898.
• [7] A. Karasińska, W. Poreda, E. Wagner-Bojakowska, Duality Principle for microscopic sets, Chapter 2 in Real functions, density topology and related topics, Łódz University Press 2011, 83–87.
• [8] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality (2nd ed.), Birkhäuser, Basel, 2009.
• [9] K. Kuratowski ,\\, Topology, Monografie Matematyczne, PWN Warszawa, 1966.
• [10] J. C. Oxtoby, Measure and Category, Springer-Verlag, New York, Heidelberg, Berlin, 1980.
• [11] I. Recław, P. Zakrzewski, Fubini properties of ideals, Real Anal. Exchange 25(2) (1999/2000), 565–578.